Optimal. Leaf size=38 \[ \frac{1}{6} \left (x^4+1\right )^{3/2}-\sqrt{x^4+1}-\frac{1}{2 \sqrt{x^4+1}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0408458, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{1}{6} \left (x^4+1\right )^{3/2}-\sqrt{x^4+1}-\frac{1}{2 \sqrt{x^4+1}} \]
Antiderivative was successfully verified.
[In] Int[x^11/(1 + x^4)^(3/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 4.04554, size = 29, normalized size = 0.76 \[ \frac{\left (x^{4} + 1\right )^{\frac{3}{2}}}{6} - \sqrt{x^{4} + 1} - \frac{1}{2 \sqrt{x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**11/(x**4+1)**(3/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0157931, size = 23, normalized size = 0.61 \[ \frac{x^8-4 x^4-8}{6 \sqrt{x^4+1}} \]
Antiderivative was successfully verified.
[In] Integrate[x^11/(1 + x^4)^(3/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.006, size = 20, normalized size = 0.5 \[{\frac{{x}^{8}-4\,{x}^{4}-8}{6}{\frac{1}{\sqrt{{x}^{4}+1}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^11/(x^4+1)^(3/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43238, size = 38, normalized size = 1. \[ \frac{1}{6} \,{\left (x^{4} + 1\right )}^{\frac{3}{2}} - \sqrt{x^{4} + 1} - \frac{1}{2 \, \sqrt{x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(x^4 + 1)^(3/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.263039, size = 26, normalized size = 0.68 \[ \frac{x^{8} - 4 \, x^{4} - 8}{6 \, \sqrt{x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(x^4 + 1)^(3/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 5.66389, size = 39, normalized size = 1.03 \[ \frac{x^{8}}{6 \sqrt{x^{4} + 1}} - \frac{2 x^{4}}{3 \sqrt{x^{4} + 1}} - \frac{4}{3 \sqrt{x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**11/(x**4+1)**(3/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.227877, size = 38, normalized size = 1. \[ \frac{1}{6} \,{\left (x^{4} + 1\right )}^{\frac{3}{2}} - \sqrt{x^{4} + 1} - \frac{1}{2 \, \sqrt{x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(x^4 + 1)^(3/2),x, algorithm="giac")
[Out]